Let us consider a set of operations
[1]}, [2]}, [3]} that transforms
the equations of motion of the lattice model
into a continuum equation for the displacement field \(u(x,t)\) .
We assume that \(u_n(t)\)  are Fourier coefficients
of the field \(\hat{u}(k,t)\)  on \([-K_0 /2, K_0 /2]\) 
that is described by the equations
\(\hat{u}(k,t) = \sum _{n=-\infty }^{+\infty } \; u_n(t) \; e^{-i k x_n} ={\cal F}_{\Delta } \lbrace u_n(t)\rbrace  ,\) 
\(u_n(t) = \frac{1}{K_0} \int _{-K_0/2}^{+K_0/2} dk \ \hat{u}(k,t) \; e^{i k x_n}={\cal F}^{-1}_{\Delta } \lbrace  \hat{u}(k,t) \rbrace  ,\) 
